You are driving on a road that has a 6% uphill grade. This means that the slope of the road is 6 100. Approximate the amount of vertical change in your position when you drive 200 feet.
> Determine whether the points are collinear. (Three points are collinear if they lie on the same line.) (0, 4), (7, -6), (-5, 11)
> Determine whether the points are collinear. (Three points are collinear if they lie on the same line.) (-2, 1), (-1, 0), (2, -2)
> Find the domain of the function. f(x) = √x + √1 − x
> You are given the dollar value of a product in 2016 and the rate at which the value of the product is expected to change during the next 5 years. Write a linear equation that gives the dollar value V of the product in terms of the year t. (Let t = 0 repr
> You are given the dollar value of a product in 2016 and the rate at which the value of the product is expected to change during the next 5 years. Write a linear equation that gives the dollar value V of the product in terms of the year t. (Let t = 0 repr
> Write the general forms of the equations of the lines that pass through the point and are a. parallel to the given line and b. perpendicular to the given line. Point: (5/6, - (1/2)) Line: 7x + 4y = 8
> Write the general forms of the equations of the lines that pass through the point and are a. parallel to the given line and b. perpendicular to the given line. Point: (3/4, 7/8) Line: 5x - 3y = 0
> Write the general forms of the equations of the lines that pass through the point and are a. parallel to the given line and b. perpendicular to the given line. Point: (2, 5) Line: x - y = -2
> Write the general forms of the equations of the lines that pass through the point and are a. parallel to the given line and b. perpendicular to the given line. Point: (-3, 2) Line: x + y = 7
> Write the general forms of the equations of the lines that pass through the point and are parallel to the given line and perpendicular to the given line. Point: (-1, 0) Line: y = -3
> Write the general forms of the equations of the lines that pass through the point and are parallel to the given line and perpendicular to the given line. Point: (-7, -2) Line: x = 1
> Use the below result to write an equation of the line with the given characteristics in general form. Point on line: (-(2/3), -2) x-intercept: (a, 0) y-intercept: (0, a) (a ≠0)
> Use the below result to write an equation of the line with the given characteristics in general form. Point on line: (9, -2) x-intercept: (2a, 0) y-intercept: (0, a) (a ≠0)
> Sketch the graph of the equation by point plotting. y = 4 − x2
> Find the domain and range of the function. f(x) = x – 2 / x+4
> Use the below result to write an equation of the line with the given characteristics in general form. x-intercept: (-2/3, 0) y-intercept: (0, -2)
> Use the below result to write an equation of the line with the given characteristics in general form. x-intercept: (2, 0) y-intercept: (0, 3)
> Show that the line with intercepts (a, 0) and (0, b) has the following equation. x/a + y/b = 1, a ≠ 0, b ≠ 0
> Write an equation for the line that passes through the points (0, b) and (3, 1).
> Find an equation of the line that passes through the points. Then sketch the line. (2, 5), (2, 7)
> Find an equation of the line that passes through the points. Then sketch the line. (3, 1), (5, 1)
> Find an equation of the line that passes through the points. Then sketch the line. (1, -2), (3, -2)
> Find an equation of the line that passes through the points. Then sketch the line. (6, 3), (6, 8)
> Find an equation of the line that passes through the points. Then sketch the line. (-3, 6), (1, 2)
> Sketch the graph of the equation by point plotting. y = 5 − 2x
> Find an equation of the line that passes through the points. Then sketch the line. (2, 8), (5, 0)
> Find the domain and range of the function. f(x) = 3/x
> Find an equation of the line that passes through the points. Then sketch the line. (-2, -2), (1, 7)
> Find an equation of the line that passes through the points. Then sketch the line. (4, 3), (0, -5)
> Sketch the graph of the equation. x + 2y + 6 = 0
> Sketch the graph of the equation. 3x – 3y + 1 = 0
> Sketch the graph of the equation. y – 1 = 3(x + 4)
> Sketch the graph of the equation. y – 2 = 3/2 (x – 1)
> Sketch the graph of the equation. y = 1 / 3 x - 1
> Sketch the graph of the equation. y = -2x + 1
> Sketch the graph of the equation by point plotting. y = (1/2)x + 2
> Sketch the graph of the equation. x = 4
> Sketch the graph of the equation. y = -3
> Find the domain and range of the function. f(x) = │x − 3│
> Find the slope and the y-intercept (if possible) of the line. y = -1
> Find the slope and the y-intercept (if possible) of the line. x = 4
> Find the slope and the y-intercept (if possible) of the line. 6x - 5y = 15
> Find the slope and the y-intercept (if possible) of the line. 5x + y = 20
> Find the slope and the y-intercept (if possible) of the line. -x + y = 1
> Find the slope and the y-intercept (if possible) of the line. y = 4x – 3
> The table shows the biodiesel productions y (in thousands of barrels per day) for the United States for 2007 through 2012. The variable t represents the time in years, with t = 7 corresponding to 2007. (Source: U.S. Energy Information Administration) a.
> Match the equation with its graph. [The graphs are labeled (a), (b), (c), and (d).] y = x3 – x
> The table shows the populations y (in millions) of the United States for 2009 through 2014. The variable t represents the time in years, with t = 9 corresponding to 2009. (Source: U.S. Census Bureau) a. Plot the data by hand and connect adjacent points
> A moving conveyor is built to rise 1 meter for each 3 meters of horizontal change. Find the slope of the conveyor. Suppose the conveyor runs between two floors in a factory. Find the length of the conveyor when the vertical distance between floors is 10
> Find the domain and range of the function. f(x) = √16 − x2
> Find an equation of the line that passes through the point and has the indicated slope. Then sketch the line. Point: (-2, 4) Slope: m = -(3/5)
> Find an equation of the line that passes through the point and has the indicated slope. Then sketch the line. Point: (3, -2) Slope: m = 3
> Find an equation of the line that passes through the point and has the indicated slope. Then sketch the line. Point: (0, 4) Slope: m = 0
> Find an equation of the line that passes through the point and has the indicated slope. Then sketch the line. Point: (1, 2) Slope: m is undefined.
> Find an equation of the line that passes through the point and has the indicated slope. Then sketch the line. Point: (-5, -2) Slope: m = 6/5
> Find an equation of the line that passes through the point and has the indicated slope. Then sketch the line. Point: (0, 3) Slope: m = 3/4
> Match the equation with its graph. [The graphs are labeled (a), (b), (c), and (d).] y = 3 − x2
> Use the point on the line and the slope of the line to find three additional points that the line passes through. (There is more than one correct answer.) Point: (-2, -1) Slope: m = 2
> Use the point on the line and the slope of the line to find three additional points that the line passes through. (There is more than one correct answer.) Point: (1, 7) Slope: m = -3
> Use the point on the line and the slope of the line to find three additional points that the line passes through. (There is more than one correct answer.) Point: (-4, 3) Slope: m is undefined
> Use the point on the line and the slope of the line to find three additional points that the line passes through. (There is more than one correct answer.) Point: (6, 2) Slope: m = 2
> Find the domain and range of the function. h(x) = −√x + 3
> Consider a polynomial f(x) with real coefficients having the property f(g(x)) = g( f(x)) for every polynomial g(x) with real coefficients. Determine and prove the nature of f(x).
> Sketch the lines through the point with the indicated slopes. Make the sketches on the same set of coordinate axes. Point (-2, 5) Slopes a. 3 b. -3 c. 1/3
> Plot the pair of points and find the slope of the line passing through them. (7/8, 3/4), (5/4, - (1/4)
> Plot the pair of points and find the slope of the line passing through them. (-(1/2, 2/3), (-(3/4), 1/6
> Plot the pair of points and find the slope of the line passing through them. (3, −5), (5, −5)
> Match the equation with its graph. [The graphs are labeled (a), (b), (c), and (d).] y = √9 – x2
> Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If f(x) = f(−x) for all x in the domain of f, then the graph of f is symmetric with respect to the y-axis.
> Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. A vertical line can intersect the graph of a function at most once.
> Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If f(a) = f(b), then a = b
> An open box of maximum volume is to be made from a square piece of material 24 centimeters on a side by cutting equal squares from the corners and turning up the sides (see figure). a. Write the volume V as a function of x, the length of the corner squ
> A right triangle is formed in the first quadrant by the x- and y-axes and a line through the point (3, 2) (see figure). Write the length L of the hypotenuse as a function of x
> Prove that the product of an odd function and an even function is odd.
> Prove that the product of two even (or two odd) functions is even.
> Evaluate the function at the given value(s) of the independent variable. Then find the domain and range. a. f (−3) b. f (0) c. f (5) d. f (10)
> Sketch the lines through the point with the indicated slopes. Make the sketches on the same set of coordinate axes. Point (3, 4) Slopes 1 -2 -(3/2)
> Find any intercepts. y2 = x3 − 4x
> Find any intercepts. y = x2 + x – 2
> A skydiver, who weighs 650 N, is falling at a constant speed with his parachute open. Consider the apparatus that connects the parachute to the skydiver to be part of the parachute. The parachute pulls upward on the skydiver with a force of 620 N. (a) Id
> Margie, who weighs 543 N, is standing on a bathroom scale that weighs 45 N. (a) With what magnitude force does the scale push up on Margie? (b) What is the interaction partner of that force? (c) With what magnitude force does the floor push up on the sca
> When a car begins to move forward, what force makes it do so? Remember that it has to be an external force; the internal forces all add to zero. How does the engine, which is part of the car, cause an external force to act on the car?
> A towline is attached between a car and a glider. As the car speeds due east along the runway, the towline exerts a horizontal force of 850 N on the glider. What is the magnitude and direction of the force exerted by the glider on the towline?
> A hummingbird is hovering motionless beside a flower. The blur of its wings shows that they are rapidly beating up and down. If the air pushes upward on the bird with a force of 0.30 N, what is the force exerted on the air by the hummingbird?
> On her way to visit Grandmother, Red Riding Hood sat down to rest and placed her 1.2 kg basket of goodies beside her. A wolf came along, spotted the basket, and began to pull on the handle with a force of 6.4 N at an angle of 25° with respect to vertical
> A barge is hauled along a straight-line section of canal by two horses harnessed to tow ropes and walking along the tow paths on either side of the canal. Each horse pulls with a force of 560 N at an angle of 15° with the centerline of the canal. Find th
> Two forces of magnitudes 3.0 N and 4.0 N act on an object. How are the directions of the two forces related if (a) the net force has magnitude 7.0 N or (b) the net force has magnitude 5.0 N? (c) What relationship between the directions gives the smallest
> Two objects, A and B, are acted on by the forces shown in the FBDs. Is the magnitude of the net force acting on object B greater than, less than, or equal to the magnitude of the net force acting on object A? Explain.
> A sailboat, tied to a mooring with a line, weighs 820 N. The mooring line pulls horizontally toward the west on the sailboat with a force of 110 N. The sails are stowed away and the wind blows from the west. The boat is moored on a still lake—no water cu
> The figure shows the quadriceps and the patellar tendons attached to the patella (the kneecap). If the tension T in each tendon is 1.30 kN, what are the magnitude and direction of the contact force F exerted on the patella by the femur? The weight of the
> A car is driving on a straight, level road at constant speed. Draw an FBD for the car, showing the significant forces that act on it.
> A man is lazily floating on an air mattress in a swimming pool. If the weight of the man and air mattress together is 806 N, what is the upward force of the water acting on the mattress?
> A person stands on the ball of one foot. The normal force due to the ground pushing up on the ball of the foot has magnitude 750 N. Ignore the weight of the foot itself. The other significant forces acting on the foot are the tension in the Achilles tend
> In an attempt to tighten the loosened steel head of a hammer, a carpenter holds the hammer vertically, raises it up, and then brings it down rapidly, hitting the bottom end of the wood handle on a two-by four board. Explain how this tightens the head bac
> Forces of magnitudes 2000 N and 3000 N act on five objects. The directions of the forces are shown in the sketches. Rank the objects according to the magnitude of the net force, from smallest to largest. Explain your reasoning.
> Vector b has magnitude 7.1 and direction 14° below the +x-axis. Vector c has x-component cx = −1.8 and y-component cy = −6.7. Compute: (a) the x- and y-components of b. (b) the magnitude and direction of c. (c) the magnitude and direction of c+b.
> In each of these, the x- and y-components of a vector are given. Find the magnitude and direction of the vector. (a) x = −5.0 cm, y = +8.0 cm. (b) Fx = +120 N, Fy = −60.0 N. (c) vx = −13.7 m/s, vy = −8.8 m/s. (d) ax = 2.3 m/s2, ay = 6.5 cm/s2.
> Find the x- and y-components of the four vectors shown in the drawing.
> Vector A has magnitude 4.0 units; vector B has magnitude 6.0 units. The angle between A and B is 60.0°. What is the magnitude of A+B?
> A vector is 20.0 m long and makes an angle of 60.0° counterclockwise from the y-axis (on the side of the −x-axis). What are the x- and y-components of this vector?
